We present a model for ruptures in an elastic medium. The basic unit i
s a plaquet on which local strain and stress tensors are assigned. We
show that our discretization naturally leads to a double-couple repres
entation of local ruptures. The stress redistribution due to ruptures
is conveniently calculated using lattice Green's functions. This descr
iption can be immediately applied to the study of earthquakes, which a
re a sequence of ruptures generated by continuous stress increase in a
medium. We show that our model is suitable for incorporating some bas
ic properties of rocks (e.g. static fatigue and healing of the fractur
ed surfaces), as well as for studying the spatial patterns of earthqua
ke activities.